On partitions of hereditary properties of graphs

Access Full Article

Abstract

top
In this paper a concept 𝓠-Ramsey Class of graphs is introduced, where 𝓠 is a class of bipartite graphs. It is a generalization of well-known concept of Ramsey Class of graphs. Some 𝓠-Ramsey Classes of graphs are presented (Theorem 1 and 2). We proved that 𝓣₂, the class of all outerplanar graphs, is not 𝓓₁-Ramsey Class (Theorem 3). This results leads us to the concept of acyclic reducible bounds for a hereditary property 𝓟 . For 𝓣₂ we found two bounds (Theorem 4). An improvement, in some sense, of that in Theorem is given.

@article{MieczysławBorowiecki2006, abstract = {In this paper a concept 𝓠-Ramsey Class of graphs is introduced, where 𝓠 is a class of bipartite graphs. It is a generalization of well-known concept of Ramsey Class of graphs. Some 𝓠-Ramsey Classes of graphs are presented (Theorem 1 and 2). We proved that 𝓣₂, the class of all outerplanar graphs, is not 𝓓₁-Ramsey Class (Theorem 3). This results leads us to the concept of acyclic reducible bounds for a hereditary property 𝓟 . For 𝓣₂ we found two bounds (Theorem 4). An improvement, in some sense, of that in Theorem is given.}, author = {Mieczysław Borowiecki, Anna Fiedorowicz}, journal = {Discussiones Mathematicae Graph Theory}, keywords = {hereditary property; acyclic colouring; Ramsey class}, language = {eng}, number = {3}, pages = {377-387}, title = {On partitions of hereditary properties of graphs}, url = {http://eudml.org/doc/270628}, volume = {26}, year = {2006},}

TY - JOURAU - Mieczysław BorowieckiAU - Anna FiedorowiczTI - On partitions of hereditary properties of graphsJO - Discussiones Mathematicae Graph TheoryPY - 2006VL - 26IS - 3SP - 377EP - 387AB - In this paper a concept 𝓠-Ramsey Class of graphs is introduced, where 𝓠 is a class of bipartite graphs. It is a generalization of well-known concept of Ramsey Class of graphs. Some 𝓠-Ramsey Classes of graphs are presented (Theorem 1 and 2). We proved that 𝓣₂, the class of all outerplanar graphs, is not 𝓓₁-Ramsey Class (Theorem 3). This results leads us to the concept of acyclic reducible bounds for a hereditary property 𝓟 . For 𝓣₂ we found two bounds (Theorem 4). An improvement, in some sense, of that in Theorem is given.LA - engKW - hereditary property; acyclic colouring; Ramsey classUR - http://eudml.org/doc/270628ER -